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Blast from the past, 2/17/07 VH

 
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shoeless



Joined: 03 Aug 2007
Posts: 13

PostPosted: Wed Aug 08, 2007 1:05 pm    Post subject: Blast from the past, 2/17/07 VH Reply with quote

Looked through the forum to see if this one had come up before, but there seems to be a big gap from about 10/06 to 5/07. Question

Anyway, I'm stuck on this one...

Code:

+-----------+---------------+-------------+
| 4   1 9   | 27   3    6   | 8    5  27  |
| 23  8 5   | 2479 19   179 | 2347 67 346 |
| 23  7 6   | 248  5    28  | 9    1  34  |
+-----------+---------------+-------------+
| 79  6 47  | 3    2    179 | 5    8  14  |
| 1   2 34  | 578  68   57  | 34   67 9   |
| 789 5 378 | 789  1689 4   | 37   2  136 |
+-----------+---------------+-------------+
| 5   4 2   | 1    7    3   | 6    9  8   |
| 6   3 78  | 2589 89   59  | 1    4  27  |
| 78  9 1   | 6    4    28  | 27   3  5   |
+-----------+---------------+-------------+

Play this puzzle online

Sure seems like I should be able to eliminate some of those 4-candidate cells. I must be missing something obvious....again. Confused Hint says 9 in r4c1, but I don't see why. Any ideas?
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Wed Aug 08, 2007 3:43 pm    Post subject: Reply with quote

shoeless, you saved my day!

no new sudokus for 5 days, what a drag...

in your position,
Quote:
Code:

+-----------+---------------+-------------+
| 4 1 9 | 27 3 6 | 8 5 27 |
| 23 8 5 | 2479 19 179 | 2347 67 346 |
| 23 7 6 | 248 5 28 | 9 1 34 |
+-----------+---------------+-------------+
| 79 6 47 | 3 2 179 | 5 8 14 |
| 1 2 34 | 578 68 57 | 34 67 9 |
| 789 5 378 | 789 1689 4 | 37 2 136 |
+-----------+---------------+-------------+
| 5 4 2 | 1 7 3 | 6 9 8 |
| 6 3 78 | 2589 89 59 | 1 4 27 |
| 78 9 1 | 6 4 28 | 27 3 5 |
+-----------+---------------+-------------+

row 6 contains a naked quad (3789)

later on watch out for some fishy/skyscrapery business in '2',
two xy wing situations, an xyz wing

boy, this one has them all ...

have fun!
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shoeless



Joined: 03 Aug 2007
Posts: 13

PostPosted: Wed Aug 08, 2007 6:16 pm    Post subject: Reply with quote

nataraj,

Thanks for the tip on the naked quad. Other than eliminating a few candidates on r6, it didn't really get me over the hump. When you say "business in 2", do you mean box 2? If so, I'm still not seeing any of the wings there. Confused
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Wed Aug 08, 2007 6:54 pm    Post subject: Reply with quote

actually, removing candidates from row 6 isn't so bad. especially the 3 in c9.

now all '3's in c9 are in box 3.

by "business in '2'" I meant the cells with candidate 2. When I don't see an x-wing or swordfish immediately I start to do quick sketches of the board with all cells containig '1', another sketch of the '2's and so on. It sounds much more tedious than it is. 4 quick lines like this:
Code:

     |     |
     |     |
--------------------
     |     |
     |     |
-------------------
     |     |
     |     |

and then a dot for each cell. Helps to spot patterns like xwing, swordfish, turbo and other fish, finned creatures and the like and all sorts of other x-cycles. Since I usually act on the first pattern I find I cannot tell whether it was the fastest route to the solution. Just _A_ route.

hope this actually helps. it started to sound a bit confusing even to me.. sorry.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Wed Aug 08, 2007 7:34 pm    Post subject: Reply with quote

the "business in 2" is an x-wing in rows 1 and 8 (removing 2 from cols 4 and 9)

removing '7' from r5c4 is more difficult.
on my drawing it looks like this


Code:

     ·*---------*
     ·     ·     
     ·o   o·o * o
     ·     ·  | 
     ·     ·  |
·····+·····+··|··
o   o·    o·  | o
     ·     ·  | 
     ·x   o·  * 
     ·     ·     
o   o·o    ·o   


"x" can see r1c4 and r5c8 which are linked by an alternating chain of strong and weak links. "strong" means there are only two cells in a unit (row, column or box) containing 7 as a candidate, meaning that when one of them is not 7 the ohter is.

"weak" link means there can be 2 or more cells so when one of them is "7" the others cannot be 7.

In this case the reasoning is as follows:
Let r1c4 be 7. Then r5c4 cannot be 7 (weak link)
but if r1c4 is not 7 then r1c9 is (strong link)
then r2c8 is not (weak link)
then r5c8 IS (strong link)
then r5c4 is NOT (weak link)

so whichever way r1c4 turn out, r5c4 cannot be 7.

The reasoning is very similar to xy chains, xy wing, xyz wing and the like.
But the real treat lies in the fact that once you draw the diagrams (not so very hard to do) the connection becomes fairly easy to spot.

I used to spend hours -well, half hours Smile - looking at the piece of paper and always missing that one xwing or swordfish or whatever.
not any more. that little # is my friend now ...
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Aug 08, 2007 9:29 pm    Post subject: Reply with quote

I believe that <7> elimination example is sometimes called a "Kite" or "2-String Kite" or "Turbot Fish," and may have other names. It is also an example of a more general method called "Color Wing." More generally still, it is a Alternate Implication Chain (AIC). Nataraj explains the logic well.

(I, too, have drawn those simple dot grids.)
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Wed Aug 08, 2007 10:06 pm    Post subject: Reply with quote

I'm not interested in this puzzle guys - just hangin around for the next VH Day. But I should mention that I made up an Excel spreadsheet to do the "pencil work" stuff and show the candidate numbers that are available in each cell. I can also click to see X's for where the individual numbers are: this helps identify the patterns.
This isn't cheating eh! It's just a tool to take out the mundane and tedious groundwork before the battle.
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shoeless



Joined: 03 Aug 2007
Posts: 13

PostPosted: Thu Aug 09, 2007 2:46 pm    Post subject: Reply with quote

I agree, nataraj's explanation of the logic was clear and made sense. It's always easy to see that stuff when someone points it out, but recognizing those patterns in the first place....that's where I have problems.

Anyway, I took your advice, tried making several grid drawings showing strong and weak links. I guess I'm still just too new at this stuff because the patterns don't jump out at me. Correct me if i'm wrong, but it seems like you need an odd number of "hops" as you progress around the chains in order to eliminate a candidate from a cell (if that makes sense). Using your example,
starting at r5c4, I'd hop to r1c4 -> r1c9 -> r2c8 -> r5c8 -> ending back at r1c4 for a total of 5 hops. Since each hop is a yes/no kind of logic, the odd yes/no's eliminate the candidate. Anyway, all I see is even hops...make sense?

After 2 days of fiddling with this puzzle on and off, I'm about ready to throw in the towel... Sad
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Aug 09, 2007 3:28 pm    Post subject: Reply with quote

Code:
 
+-----------+---------------+-------------+
| 4   1 9   | 27a  3    6   | 8    5  27A |
| 23  8 5   | 2479 19   179 | 2347 67B346 |
| 23  7 6   | 248  5    28  | 9    1  34  |
+-----------+---------------+-------------+
| 79  6 47  | 3    2    179 | 5    8  14  |
| 1   2 34  | 578  68   57  | 34   67b9   |
| 789 5 378 | 789  1689 4   | 37   2  136 |
+-----------+---------------+-------------+
| 5   4 2   | 1    7    3   | 6    9  8   |
| 6   3 78  | 2589 89   59  | 1    4  27  |
| 78  9 1   | 6    4    28  | 27   3  5   |
+-----------+---------------+-------------+


As Asellus said, this is known by many names and it's a common occurrence in many puzzles, though not always useful. It is two strongly linked chains on <7> (one marked A-a, one marked B-b) connected by a weak link (the cells marked A & B). Since A & B are both in box 3, they both cannot be true, which means that at least one of a & b are. Any cell that sees both a & b cannot be <7>.
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shoeless



Joined: 03 Aug 2007
Posts: 13

PostPosted: Thu Aug 09, 2007 3:36 pm    Post subject: Reply with quote

TKiel wrote:

As Asellus said, this is known by many names and it's a common occurrence in many puzzles, though not always useful. It is two strongly linked chains on <7> (one marked A-a, one marked B-b) connected by a weak link (the cells marked A & B). Since A & B are both in box 3, they both cannot be true, which means that at least one of a & b are. Any cell that sees both a & b cannot be <7>.


Yeah, I see how that works, but it doesn't exactly bust this puzzle open...

Code:

+-----------+-------------+------------+
| 4   1 9   | 27   3  6   | 8   5  27  |
| 23  8 5   | 479  19 179 | 247 67 346 |
| 23  7 6   | 48   5  28  | 9   1  34  |
+-----------+-------------+------------+
| 79  6 47  | 3    2  179 | 5   8  14  |
| 1   2 34  | 58   68 57  | 34  67 9   |
| 789 5 378 | 789  16 4   | 37  2  16  |
+-----------+-------------+------------+
| 5   4 2   | 1    7  3   | 6   9  8   |
| 6   3 78  | 2589 89 59  | 1   4  27  |
| 78  9 1   | 6    4  28  | 27  3  5   |
+-----------+-------------+------------+

Play this puzzle online at the Daily Sudoku site
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Aug 09, 2007 7:02 pm    Post subject: Reply with quote

shoeless,
Look at box 4 and notice how all the 8's are on row 6 (gets rid of 8 in r6c4).
Then (with 79 as candidates in r6c4) there is an xy wing (pivot r5c6) 79-57-59 eliminating 9 from r4c6 and r8c4.

Once you have eliminated 9 from r2c4 (happens a few steps later), there is an XYZ wing in box 3:

47 in r2c4 and 247 in r2c7 point the gun, 27 in r1c9 pulls the trigger, and 7 in r2c8 drops dead. The shape looks like a gun backfiring:
Code:

          *
         /
*-------*->o


As I said before: this puzzle has them all. Doesn't yield to one attack only.
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shoeless



Joined: 03 Aug 2007
Posts: 13

PostPosted: Thu Aug 09, 2007 7:30 pm    Post subject: Reply with quote

nataraj,

Thanks! I caught the 8's on row 6 shortly after I made my post. It was the 79-57-59 xy wing that was eluding me. It fell into place once you pointed that out. In general, how do you spot those on your grid drawings? As I understood you before, I made a grid drawing for each digit. Do you overlay them somehow to see the xy wings? Thanks for all your help on this one.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Aug 09, 2007 7:47 pm    Post subject: Reply with quote

glad I could help.

The xy(whatever variety) and the drawings are diffent approaches.

The drawings show ALL occurrences of ONE number, like all sevens, no matter how many other candidates are in the cell. The links work on purely yes/no relationships ("if 7 is in cell a, then NOT in B,C,D")

I have not yet found a similar graphic approach to xy-relationships.
Tried to connect cells with lines once, but that became very messy.

XY-chains/wings work with bi-value cells (cell A is either 5 or 7) and take the form "if not A then B".

Since bi-value cells are easy to see and usually there aren't that many of them, it is just a question of taking them one by one and see if a wing exists.

cheers
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Aug 09, 2007 9:43 pm    Post subject: Reply with quote

There are programs that can be used to help one solve sudoku. Many of them have settings that can be adjusted to be of more or less help, depending on the requirements of the user. The one I use is called Simple Sudoku (available here ) and is free. In my opinion they are invaluable in helping to solve puzzles, such as this one, that require more advanced techniques, which can be extremely difficult to spot. SS can filter on each digit individually (useful for searching for strongly linked cells) or on bi-value cells (useful for searching for XY-wings/chains). Or one can use it for nothing but maintenance (keeping the pencil marks up-to-date). It really is up to the user. And I know that there are many others out there that will do much the same thing.
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